If Kelly received 1/3 times more votes than Mike in a studen

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Fri Jun 14, 2019 6:14 pm

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If Kelly received 1/3 times more votes than Mike in a student election, which of the following could have been the total number of votes cast for the two candidates?

A. 12
B. 13
C. 14
D. 15
E. 16

OA C

Source: Manhattan Prep

Source: Beat The GMAT — Problem Solving | Fri Jun 14, 2019 6:14 pm

swerve: Legendary Member; Posts: 2604; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

by swerve » Sun Jun 16, 2019 3:16 pm

The question should say $\frac{1}{3}$ TIMES more votes.

$K = M + \frac{1}{3}M$
$K = \frac{4}{3}M$
$M+K=M+\frac{4}{3}M=$Total
Total $= \frac{7}{3}M$
$M=\frac{3}{7}$ Total

Total must be a multiple of 7 because Mary can't receive fractional numbers of votes.

The only option that is a multiple of 7 is 14. Hence, __C__ is the correct answer.

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by Scott@TargetTestPrep » Fri Jun 21, 2019 6:48 pm

BTGmoderatorDC wrote:If Kelly received 1/3 times more votes than Mike in a student election, which of the following could have been the total number of votes cast for the two candidates?

A. 12
B. 13
C. 14
D. 15
E. 16

OA C

Source: Manhattan Prep

If we let k = the number of votes Mike received, then (4/3)k = the number of votes Kelly received. Thus, they received a total of k + 4k/3 = 3k/3 + 4k/3 = 7k/3 votes.

Since 7k/3 has to be an integer, k can be any multiple of 3. Furthermore, 7k/3 is a multiple of 7 since k/3 is an integer. The only multiple of 7 among the answer choices is 14.

Answer: C

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